にて is often considered as its own stand-alone particle, despite originally being a mix of に, and the conjunction particle, て. When combined, にて becomes a formal case-marking particle that is used in the same way as で. This means that it can convey the meaning of ‘with (A)’, ‘by (A)’, ‘at (A)’, or ‘using (A)’.
にて will primarily appear following nouns that illustrate a means, method, time, location, reason, or origin that the speaker wants to highlight.

• 明日（あす）は金（きん）時計（どけい）にて集合（しゅうごう）しましょう。
  Let's meet tomorrow at the Golden Clock.
• 当店（とうてん）は午前（ごぜん）9時（じ）にて開店（かいてん）いたします。
  This store will open at 9:00 a.m.
• 予約（よやく）をされる場合（ばあい）は電話（でんわ）にてご連絡（れんらく）ください。
  If you want to make a reservation, please make one using the phone.

As this grammar structure is formal, it will primarily be seen in writing, or heard in announcements. で will be the far more natural choice in casual conversation.